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<a href="_approximate_kernel_expansion_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span><span class="comment">//===========================================================================</span><span class="comment"></span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno">    2</span><span class="comment">/*!</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno">    3</span><span class="comment"> * </span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno">    4</span><span class="comment"> *</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno">    5</span><span class="comment"> * \brief       The k-means clustering algorithm.</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno">    6</span><span class="comment"> * </span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno">    7</span><span class="comment"> * </span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno">    8</span><span class="comment"> *</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno">    9</span><span class="comment"> * \author      T. Glasmachers</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno">   10</span><span class="comment"> * \date        2011</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno">   11</span><span class="comment"> *</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno">   12</span><span class="comment"> *</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span><span class="comment"> * \par Copyright 1995-2017 Shark Development Team</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span><span class="comment"> * </span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span><span class="comment"> * &lt;BR&gt;&lt;HR&gt;</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span><span class="comment"> * This file is part of Shark.</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span><span class="comment"> * &lt;https://shark-ml.github.io/Shark/&gt;</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span><span class="comment"> * </span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span><span class="comment"> * Shark is free software: you can redistribute it and/or modify</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span><span class="comment"> * it under the terms of the GNU Lesser General Public License as published </span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span><span class="comment"> * by the Free Software Foundation, either version 3 of the License, or</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span><span class="comment"> * (at your option) any later version.</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span><span class="comment"> * </span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span><span class="comment"> * Shark is distributed in the hope that it will be useful,</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span><span class="comment"> * but WITHOUT ANY WARRANTY; without even the implied warranty of</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span><span class="comment"> * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span><span class="comment"> * GNU Lesser General Public License for more details.</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span><span class="comment"> * </span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span><span class="comment"> * You should have received a copy of the GNU Lesser General Public License</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span><span class="comment"> * along with Shark.  If not, see &lt;http://www.gnu.org/licenses/&gt;.</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span><span class="comment"> *</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span><span class="comment"> */</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span><span class="comment">//===========================================================================</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span> </div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span> </div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span><span class="preprocessor">#ifndef SHARK_ALGORITHMS_APPROXIMATE_KERNEL_EXPANSION_H</span></div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span><span class="preprocessor">#define SHARK_ALGORITHMS_APPROXIMATE_KERNEL_EXPANSION_H</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span> </div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span><span class="preprocessor">#include &lt;<a class="code" href="_d_l_l_support_8h.html">shark/Core/DLLSupport.h</a>&gt;</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span><span class="preprocessor">#include &lt;<a class="code" href="_random_8h.html">shark/Core/Random.h</a>&gt;</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span><span class="preprocessor">#include &lt;<a class="code" href="_kernel_expansion_8h.html">shark/Models/Kernels/KernelExpansion.h</a>&gt;</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceshark.html" title="AbstractMultiObjectiveOptimizer.">shark</a>{<span class="comment"></span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span><span class="comment">/// \brief Approximates a kernel expansion by a smaller one using an optimized basis.</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span><span class="comment">///</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span><span class="comment">/// often, a kernel expansion can be represented much more compactly when the points defining the basis of the kernel</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span><span class="comment">/// expansion are not fixed.  The resulting kernel expansion can be evaluated much quicker than the original</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span><span class="comment">/// when k is small compared to the number of the nonzero elements in the weight vector of the supplied kernel expansion.</span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span><span class="comment">///</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span><span class="comment">/// Given a kernel expansion with weight matrix alpha and Basis B of size m, finds a new weight matrix beta and Basis Z with k vectors</span></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span><span class="comment">/// so that the difference of the resulting decision vectors is small in the RKHS defined by the supplied kernel.</span></div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span><span class="comment">///</span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span><span class="comment">/// The algorithm proceeds by first performing a kMeans clustering as a good initialization. This initial guess is then optimized</span></div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span><span class="comment">/// by finding the closest weight vector to the original vector representable by the basis. Using this estimate, the basis</span></div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span><span class="comment">/// can then be optimized.</span></div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span><span class="comment">///</span></div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span><span class="comment">/// The supplied kernel must be dereferentiable wrt its input parameters which excludes all kernels not defined on RealVector</span></div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span><span class="comment">///</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span><span class="comment">/// The algorithms is O(k^3 + k m) in each iteration.</span></div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span><span class="comment">///</span></div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span><span class="comment">/// \param rng the Rng used for the kMeans clustering</span></div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span><span class="comment">/// \param model the kernel expansion to approximate</span></div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span><span class="comment">/// \param k the number of basis vectors to be used by the approximation</span></div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span><span class="comment">/// \param precision target precision of the gradient to be reached during optimization</span></div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"><a class="line" href="namespaceshark.html#ac5c9544e69ebe2a80b6b14eff23108c8">   64</a></span><span class="comment"></span><a class="code hl_define" href="_d_l_l_support_8h.html#a54b73283f7f70b27fbd8ac5d4621827f" title="Defines SHARK_COMPILE_DLL.">SHARK_EXPORT_SYMBOL</a> <a class="code hl_class" href="classshark_1_1_kernel_expansion.html" title="Linear model in a kernel feature space.">KernelExpansion&lt;RealVector&gt;</a> <a class="code hl_function" href="namespaceshark.html#ac5c9544e69ebe2a80b6b14eff23108c8" title="Approximates a kernel expansion by a smaller one using an optimized basis.">approximateKernelExpansion</a>(</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>    random::rng_type&amp; rng,</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>    <a class="code hl_class" href="classshark_1_1_kernel_expansion.html" title="Linear model in a kernel feature space.">KernelExpansion&lt;RealVector&gt;</a> <span class="keyword">const</span>&amp; model,</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>    std::size_t k,</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    <span class="keywordtype">double</span> precision = 1.e-8</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>);</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span> </div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>} <span class="comment">// namespace shark</span></div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span><span class="preprocessor">#endif</span></div>
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